U.S. patent application number 16/956940 was filed with the patent office on 2021-01-07 for method and device for measuring fat in milk.
The applicant listed for this patent is Endress+Hauser Flowtec AG. Invention is credited to Wolfgang Drahm, Stefan Pfluger, Hao Zhu.
Application Number | 20210003491 16/956940 |
Document ID | / |
Family ID | |
Filed Date | 2021-01-07 |
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United States Patent
Application |
20210003491 |
Kind Code |
A1 |
Pfluger; Stefan ; et
al. |
January 7, 2021 |
METHOD AND DEVICE FOR MEASURING FAT IN MILK
Abstract
Method for continuous determining of fat content of milk having
variable solids fractions and flowing with variable gas content in
a pipeline, comprising: ascertaining a value for velocity of sound
and an average density value for milk flowing in the pipeline based
on eigenfrequencies of at least two bending oscillation wanted
modes of measuring tubes of a densimeter arranged in the pipeline;
ascertaining a value for static pressure in the pipeline by means
of a pressure sensor connected to the pipeline; ascertaining a
value for gas volume fraction based on the value for the velocity
of sound, the value for the average density and the value for the
pressure; ascertaining a value of density of milk flowing in the
pipeline without gas content based on the value for the average
density and based on the value for the gas volume fraction;
ascertaining a value for permittivity of milk flowing in the
pipeline based on at least one measuring of propagation velocity
and/or absorption of microwaves in the milk by means of a microwave
sensor arranged in the pipeline; and calculating fat fraction based
on the value of the density of the milk flowing in the pipeline
without gas content and the value for the effective
permittivity.
Inventors: |
Pfluger; Stefan; (Munchen,
DE) ; Drahm; Wolfgang; (Erding, DE) ; Zhu;
Hao; (Freising, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Endress+Hauser Flowtec AG |
Reinach |
|
CH |
|
|
Appl. No.: |
16/956940 |
Filed: |
December 10, 2018 |
PCT Filed: |
December 10, 2018 |
PCT NO: |
PCT/EP2018/084185 |
371 Date: |
June 22, 2020 |
Current U.S.
Class: |
1/1 |
International
Class: |
G01N 9/00 20060101
G01N009/00; G01N 22/00 20060101 G01N022/00; G01N 33/06 20060101
G01N033/06; G01F 1/84 20060101 G01F001/84; G01F 1/74 20060101
G01F001/74; G01K 13/02 20060101 G01K013/02; G01L 19/00 20060101
G01L019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 22, 2017 |
DE |
102017131269.2 |
Claims
1. Method for continuous determining of fat content of milk having
variable solids fractions and flowing with variable gas content in
a pipeline, comprising: ascertaining a value for velocity of sound
and an average density value for milk flowing in the pipeline based
on eigenfrequencies of at least two bending oscillation wanted
modes of measuring tubes of a densimeter arranged in the pipeline;
ascertaining a value for static pressure in the pipeline by means
of a pressure sensor connected to the pipeline; ascertaining a
value for gas volume fraction based on the value for the velocity
of sound, the value for the average density and the value for the
pressure; ascertaining a value of density of milk flowing in the
pipeline without gas content based on the value for the average
density and based on the value for the gas volume fraction;
ascertaining a value for permittivity of milk flowing in the
pipeline based on at least one measuring of propagation velocity
and/or absorption of microwaves in the milk by means of a microwave
sensor arranged in the pipeline; and calculating fat fraction based
on the value of the density of the milk flowing in the pipeline
without gas content and the value for the effective
permittivity.
2. Method as claimed in claim 1, wherein, for the calculating, the
milk is modeled as a three component system, wherein the components
comprise fat, water and fat-free solids.
3. Method as claimed in claim 2, wherein the solids comprise
proteins and carbohydrates, especially mainly lactose.
4. Method as claimed in one of the preceding claims, wherein
density of milk flowing in the pipeline without gas content is
modeled as a function, for example, a linear function, of
concentration of the components contained in the milk with density
values of pure components as weighting factors; wherein effective
permittivity of milk flowing in the pipeline is modeled taking into
consideration gas content as a function of concentration of the
components contained in the milk and permittivity values of the
pure components; and wherein concentration of the components is
ascertained, which lead to the ascertained values of the density
and the effective permittivity of the milk.
5. Method as claimed in one of the preceding claims, wherein the
determining of the permittivity occurs in the presence of at least
one frequency above 1 GHz, especially above 2 GHz, for example, at
2.45 GHz.
6. Method as claimed in one of the preceding claims, further
comprising: measuring temperature of milk flowing in the pipeline;
and ascertaining temperature dependent values for density and/or
permittivity of the components contained in the milk.
7. Method as claimed in one of the preceding claims, wherein the
densimeter comprises a Coriolis mass flowmeter, wherein the method
further comprises: ascertaining mass flow, volume flow and/or fat
flow and/or solids flow and/or fat-free solids flow and/or water
flow in the pipeline.
8. Measuring arrangement for determining fat content of milk in a
pipeline, especially with the method as claimed in one of the
preceding claims, comprising: a densimeter having at least one
oscillatable measuring tube for ascertaining a density measured
value and a sound velocity measured value of a medium contained in
the measuring tube based on at least wanted mode eigenfrequencies
of at least two bending oscillation wanted modes; a pressure sensor
for measuring an absolute pressure of a medium; a microwave sensor
for ascertaining absorption and/or propagation velocity of
microwave signals in a medium; and a computer unit for calculating
fat content based on measured values of the densimeter, the
pressure sensor and the microwave sensor.
9. Measuring arrangement as claimed in claim 8 for determining fat
content of milk in a pipeline, wherein the densimeter, the pressure
sensor and the microwave sensor are installed in the pipeline.
10. Measuring arrangement as claimed in claim 8 or 9, wherein the
densimeter comprises a Coriolis mass flowmeter.
Description
[0001] The present invention relates to a method and to a device
for milk fat measurement:
[0002] Milk and intermediates won therefrom can be described as
mixtures of various components, mainly water, milk fat and solids,
wherein the solids comprise essentially proteins, carbohydrates
(among these especially lactose) and, in small amounts,
minerals.
[0003] During the processing chain beginning with raw milk and
extending to the manufacture of milk products, the percentages of
these components are important parameters for controlling the
processes, for process- and quality checking, and for balancing
product streams. Usual practice is to determine the percentages
using laboratory samples and standard methods. This means that only
a few samples can be evaluated, and an analytical result is
obtained only with significant delay following the sample
taking.
[0004] A process-near spectroscopic analysis in the infrared region
with automated sample taking is, indeed, possible, however, this
is, firstly, very costly and, second, only based on the low volume
of the samples taken in comparatively large time intervals. For
process control, such an analysis is, consequently, only
conditionally suitable.
[0005] A density measurement, e.g. by means of Coriolis flowmeter,
is, indeed, suitable as inline measuring for continuous process
monitoring, and can also be used for determining the fat content,
or the solids percentages, of milk when the assumption of a given
ratio of the solids percentages of fat, carbohydrates (especially
lactose), proteins, etc. is justified. With declining validity of
this assumption, the measuring result becomes correspondingly
inaccurate.
[0006] Another difficulty with the determining of fat content with
a Coriolis flowmeter results from microbubbles of air distributed
in the milk, which, on the one hand, lessen the effective density
and, on the other hand, due to oscillations of the now compressible
milk compared with the measuring tube, lead to changed
relationships between eigenfrequencies of the oscillating measuring
tubes of the flowmeter and the density of the measured substance in
the measuring tubes. The limited suitability of Coriolis mass
flowmeters for determining the composition of liquids containing
gas is described, for example, in U.S. Pat. No. 7,363,800 B2. This
teaches an arrangement with, firstly, a microwave sensor for
ascertaining dielectric parameters of a medium, second a Coriolis
mass flowmeter, third an independent sensor for determining the gas
fraction of the medium and fourth a signal processing unit for
processing the signals of the different sensors. Such is, however,
a complex and costly device.
[0007] It is, consequently, an object of the present invention to
provide a method and a corresponding measuring arrangement for
reliable, continuous measuring of the fat fraction of milk also in
the case of variable solids fractions and variable gas content.
[0008] The object is achieved according to the invention by the
method as defined in independent claim 1 and the measuring
arrangement as defined in independent claim 8.
[0009] The method of the invention for continuous determining of
fat content of milk having variable solids fractions and flowing
with variable gas content in a pipeline, comprises:
[0010] ascertaining a value for velocity of sound and an average
density value for milk flowing in the pipeline based on
eigenfrequencies of at least two bending oscillation wanted modes
of measuring tubes of a densimeter arranged in the pipeline;
[0011] ascertaining a value for static pressure in the pipeline by
means of a pressure sensor connected to the pipeline;
[0012] ascertaining a value for gas volume fraction based on the
value for the velocity of sound, the value for the average density
and the value for the pressure;
[0013] ascertaining a value of density of milk flowing in the
pipeline without gas content based on the value for the average
density and based on the value for the gas volume fraction;
[0014] ascertaining a value for permittivity of milk flowing in the
pipeline based on at least one measuring of propagation velocity
and/or absorption of microwaves in the milk by means of a microwave
sensor arranged in the pipeline; and
[0015] calculating fat fraction based on the value of the density
of the milk flowing in the pipeline without gas content and the
value for the effective permittivity.
[0016] In a further development of the invention, the milk is
modeled as a three components system, wherein the components
comprise fat, water and fat-free solids.
[0017] In a further development of the invention, the solids
comprise proteins and carbohydrates, among these especially
lactose.
[0018] In a further development of the invention, the density of
the milk flowing in the pipeline without gas content is modeled as
a function, for example, a linear function, of concentration of the
components contained in the milk with density values of pure
components as weighting factors; wherein effective permittivity of
milk flowing in the pipeline is modeled taking into consideration
gas content as a function of concentration of the components
contained in the milk and permittivity values of the pure
components; and wherein concentration of the components is
ascertained, which lead to the ascertained values of the density
and the effective permittivity of the milk.
[0019] In a further development of the invention, the determining
of the permittivity occurs in the presence of at least one
frequency above 1 GHz, especially above 2 GHz, for example, at 2.45
GHz.
[0020] In a further development of the invention, the method
further includes measuring temperature of milk flowing in the
pipeline; and ascertaining temperature dependent values for density
and/or permittivity of the components contained in the milk.
[0021] In a further development of the invention, the densimeter
comprises a Coriolis mass flowmeter, wherein the method further
comprises:
[0022] ascertaining mass flow, volume flow and/or fat flow in the
pipeline.
[0023] The measuring arrangement of the invention for determining
fat content of milk in a pipeline, especially with the method as
claimed in one of the preceding claims, comprises:
[0024] a densimeter having at least one oscillatable measuring tube
for ascertaining a density measured value and a sound velocity
measured value of a medium contained in the measuring tube based on
at least wanted mode eigenfrequencies of at least two bending
oscillation wanted modes;
[0025] a pressure sensor for measuring an absolute pressure of a
medium;
[0026] a microwave sensor for ascertaining absorption and/or
propagation velocity of microwave signals in a medium; and
[0027] a computer unit for calculating fat content based on
measured values of the densimeter, the pressure sensor and the
microwave sensor.
[0028] In a further development of the invention, the densimeter,
the pressure sensor and the microwave sensor are installed in the
pipeline.
[0029] In a further development of the invention, the densimeter
comprises a Coriolis mass flowmeter.
[0030] The invention will now be explained in greater detail based
on the example of an embodiment shown in the drawing. The figures
of the drawing show as follows:
[0031] FIG. 1: a flow diagram of an example of an embodiment of the
method of the invention;
[0032] FIG. 2: a more detailed flow diagram of an example of an
embodiment of a first subprocess of the method of the
invention;
[0033] FIG. 3: a more detailed flow diagram of an example of an
embodiment of a second subprocess of the method of the invention;
and
[0034] FIG. 4: a schematic view of an example of an embodiment of a
device of the invention.
[0035] The components of milk can essentially be summarized in four
groups, namely water, fat, protein and carbohydrates, wherein the
latter comprise, for example, more than 95% lactose and small
portions of glucose and galactose. Additionally, as a function of
physical process conditions, especially as a function of existing
flow conditions, air inclusions can be present in the form of
microbubbles, which are to be taken into consideration in an
analysis. The following table presents, by way of example, the
physical properties of the components and air:
TABLE-US-00001 density .rho. [g/cm.sup.2] relative permittivity @
20.degree. C. .epsilon.'(f = 2.45 GHz) @ 20.degree. C. water 0.998
.sup.[1] 78 .sup.[2] fat 0.931 .sup.[1] 2.6 .sup.[2] protein 1.451
.sup.[1] 1.6 .sup.[2] carbohydrates 1.545 .sup.[1] 1.9 .sup.[2]
(lactose) air 0.0012 .sup. 1.0
[0036] With the help of these variables, the effective density and
permittivity of the mixture, in each case, as a function of
fractions a.sub.i of the components can be given as:
.rho..sub.milk with air=f((1-a.sub.air) a.sub.water, (1-a.sub.air)
a.sub.fat, (1-a.sub.air) a.sub.SNF, a.sub.air)
.SIGMA.'.sub.eff=f((1-a.sub.air) a.sub.water, (1-a.sub.air)
a.sub.fat, (1-a.sub.air) a.sub.SNF, .alpha.)
[0037] The air fraction a.sub.air can be ascertained by means of
the densimeter and the auxiliary variable, pressure, and is taken
into consideration in the equations as a known parameter. These
relationships hold naturally also in the case of processes, in
which air fractions are, process related, not present
(a.sub.air=0).
[0038] Since both the density as well as also the permittivity of
carbohydrates and proteins are almost the same, these can
essentially be combined without problem as one component, fat-free
solids (i.e. Solids-NonFat (SNF)) and be taken into consideration
by calculation with average density and permittivity, which results
using a typical mixing proportion of the two components in milk. In
the case of cow milk, this would be according to Wikipedia
approximately 58% carbohydrates (96% of which is lactose) and 42%
proteins.
[0039] The average density can essentially be calculated as a
weighted average of the individual densities.
[0040] A typical mixing equation, in order to determine '.sub.eff
in a mixture of a plurality of components, is the Bruggemann
formula:
MG - h MG + 2 h = n = 1 N f n n - h n + 2 h ##EQU00001##
[0041] In such case:
[0042] .sub.MG: '.sub.eff
[0043] .sub.h: permittivity of the matrix phase (water)
[0044] .sub.n: permittivity of the additives (fat, SNF, air)
[0045] f.sub.n: volume fractions of the various components
[0046] [formula taken from V Markel--Introduction to the Maxwell
Garnett Approximation, Journal of the Optical Society of American
A]
[0047] There results:
.rho..sub.milk=f(a.sub.water, a.sub.fat, a.sub.SNF) (Eq1)
.SIGMA.'.sub.eff=f((1-a.sub.air) a.sub.water, (1-a.sub.air)
a.sub.fat, (1-a.sub.air) a.sub.SNF, a.sub.air) (Eq2)
[0048] wherein a.sub.air is the volume fraction of the gas
content.
[0049] A third equation results from the sum of the volume
fractions:
a.sub.water+a.sub.fat+a.sub.SNF=1 (Eq3)
[0050] There results three equations with three unknowns, with
which the determining of the fractions of water, fat, and fat-free
solids is possible without other assumptions.
[0051] In particular, density and permittivity depend on
temperature and the permittivity on the measuring frequency. A
temperature measurement for taking into consideration the
temperature dependencies of the material properties in the solution
of the above system of equations enables a desired accuracy.
[0052] As shown in FIG. 1, the method 100 begins with a first step
110 of determining the density of the milk .rho..sub.milk free of
air fractions. This is performed by ascertaining the average
density, thus, the density of the milk with air .rho..sub.milk with
air, ascertaining the air fraction a.sub.air and correcting the
density by removing the air fraction.
[0053] In a second step 120, there follows the determining of the
effective permittivity .SIGMA.'.sub.eff, this being accomplished by
measuring the propagation properties of an electromagnetic wave in
the milk.
[0054] In a third step 130, the system of equations Eq1, Eq2, Eq3
is solved, in order to determine the fat fraction and, in given
cases, the fractions of other components.
[0055] As shown in FIG. 2a, the step 110 is subdivided into steps
as follows:
[0056] In a step 111, there occurs the determining of the
eigenfrequencies of the f.sub.1-bending oscillation mode and the
f.sub.3-bending oscillation mode of a Coriolis mass flow measuring
transducer, which here is also applied for density measurement. For
this, the f.sub.1-bending oscillation mode and the f.sub.3-bending
oscillation mode especially can be simultaneously excited. By
maximizing the ratio of the oscillation amplitude to the mode
specific excitation power by varying the excitation frequencies,
the sought eigenfrequencies can be ascertained.
[0057] Based on the ascertained eigenfrequencies f.sub.i, in a step
112, preliminary density values .rho..sub.1 and .rho..sub.3 are
determined as:
.rho. i = c 0 i + c 1 i 1 f i 2 + c 2 i 1 f i 4 , ##EQU00002##
[0058] wherein c.sub.oi, c.sub.1i, and c.sub.2i, are mode dependent
coefficients.
[0059] In a step 113, there occurs the determining of the velocity
of sound of the gas-containing liquid and, in given cases, a
correction term for the density measurement.
[0060] Then, in a step 114, by means of the velocity of sound and a
pressure measurement value, a gas volume fraction a.sub.air is
calculated, and the density of the milk minus the air is
calculated, such as explained in greater detail below.
[0061] As shown in FIG. 2b, step 113 includes for determining the
correction term, firstly, in a step 1131, calculating the ratio V
of the preliminary density values, thus, for example, division of
the preliminary density values .rho..sub.1 and .rho..sub.3 to form
V:=.rho..sub.1/.rho..sub.3.
[0062] Then, in a step 1132, a value of the velocity of sound c is
determined, which with the measured eigenfrequencies f.sub.1 and
f.sub.3 of the bending oscillation modes leads in the following
equation to the observed ratio V of the preliminary density
values:
( 1 + r ( g c f 1 ) 2 - b ) ( 1 + r ( g c f 3 ) 2 - b ) = V
##EQU00003##
[0063] wherein r is, for instance, 0.84, b=1 and g is a measuring
tube dependent, proportionality factor between velocity of sound
and resonant frequency, which can, for example, assume a value of
10/m. The value of the velocity of sound, which fulfills the above
equation, is the sought value for the velocity of sound of the
gas-containing liquid.
[0064] Based on the ascertained sound velocity value, then in step
1133 of the method in FIG. 2b a mode specific correction term
K.sub.i for the resonator effect can be calculated:
K i := ( 1 + r ( g c f i ) 2 - 1 ) . ##EQU00004##
[0065] A density value for the air containing milk .rho..sub.milk
with air can, finally, be calculated in step 1134 as:
.rho. milk with air = .rho. i K i ( M1 ) ##EQU00005##
[0066] The determining of air fraction and the calculating of the
density of the air-free milk in step 114 is shown in FIG. 2c in
greater detail and is based on the following relationship between
the velocity of sound of a gas-containing liquid and additional
parameters:
c = [ .alpha. c air 2 + ( 1 - a air ) 2 c milk 2 + .alpha. ( 1 - a
air ) .rho. milk .gamma. p ] - 1 2 ( C 1 ) ##EQU00006##
[0067] In such case, a.sub.air is the air volume fraction,
c.sub.air the velocity of sound in air, c.sub.milk the velocity of
sound in milk without air, .gamma. the adiabatic coefficient for
air, p the current pressure of the air-containing milk and
.rho..sub.milk the density of the milk without air.
[0068] The density of the air-containing milk results as the
weighted sum of the individual densities. Insofar as the density of
air at standard pressure lies, for instance, three orders of
magnitude below the density of pure milk, and the volume fraction
of the air lies in the order of magnitude of a few %, the density
of milk with air can be estimated as follows:
.rho..sub.milk with
air=.rho..sub.milk(1-a.sub.air)+.rho..sub.g.alpha.
.rho..sub.milk with air.apprxeq..rho..sub.milk(1-a.sub.air)
(M2)
[0069] Therewith, the equation C1 for the velocity of sound can be
written as:
c = [ a air c air 2 + ( 1 - a air ) 2 c milk 2 + a air .rho. milk
with air .gamma. p ] - 1 2 ##EQU00007##
[0070] By neglecting the square term in a.sub.air, there
results:
c = [ a air c air 2 + 1 - 2 a air c milk 2 + a air .rho. milk with
air .gamma. p ] - 1 2 ##EQU00008##
[0071] Solving for a.sub.air gives for the air volume fraction a
value of
a air = 1 c milk with air 2 - 1 c milk 2 1 c milk with air 2 - 2 c
milk 2 + .rho. milk with air .gamma. p ##EQU00009##
[0072] Actually the denominator is, in the pressure range relevant
for milk processing, essentially dominated by the third term, so
that the following approximation results:
a air .apprxeq. .gamma. p .rho. milk with air ( 1 c milk with air 2
- 1 c milk 2 ) ( A1 ) ##EQU00010##
[0073] Here, a reference value can be used for the velocity of
sound c.sub.milk in pure milk without air.
[0074] As shown in FIG. 2c, for determining the air fraction in
step 1141 a pressure value of the gas-containing liquid is
ascertained, which reigns in the milk at the point in time of
measuring the eigenfrequencies f.sub.1 and f.sub.3, in order that
with equation M1 the density .rho..sub.milk with air as well as
with equation C1 the velocity of sound of the air-containing milk
c.sub.milk with air can be ascertained.
[0075] For the adiabatic coefficient .gamma., it holds that:
[0076] .gamma.=c.sub.p/c.sub.v=(f+2)/f, wherein f is the number of
molecular degrees of freedom of the gas, which amounts at room
temperature, for example, to 1.4 for nitrogen and dry air.
[0077] In a step 1142, then based on the pressure measured value,
the above ascertained density of the air-containing milk
.rho..sub.milk with air as well as the above ascertained velocity
of sound of the air-containing milk c.sub.milk with air, the air
volume fraction a.sub.air is calculated with equation A1.
[0078] In a step 1143, there follows the calculating of the sought
density .rho..sub.milk for the air-free milk:
.rho. milk .apprxeq. .rho. milk with air 1 1 - aair ( M3 )
##EQU00011##
[0079] This provides the first measured variable, in order to solve
the system of equations Eq1, Eq2, Eq3.
[0080] The second step 120 will now be described, in which the
second measured variable, namely the relative permittivity, is
ascertained.
[0081] Basis for such is a measurement 121 of the propagation
properties of an electromagnetic wave (amplitude and phase of the
received signal relative to the transmitted signal) within the
medium in the pipeline between a transmitting antenna and a
receiving antenna separated with a separation d. This measurement
121 can be performed with electromagnetic waves of different
frequency f, so that a transfer function in the frequency domain
S(f) within a band from e.g. 2 GHz-4 GHz is ascertained at 122.
[0082] In practical measuring systems, the measured spectrum S(f)
does not contain exclusively the (medium dependent) propagation
properties in the distance between the transmitting- and receiving
antennas, but, instead, also the attenuation and phase rotation of
the antennas, connection cable as well as transition locations.
Added to this, in given cases, are the influences of multiple
reflections in the region of the connection cable. By suitable
reference measurements, these influences can be largely
characterized and, as a result, measurements compensated at 123, so
that only the relevant part of the transfer function between
transmitting- and receiving antenna remains.
[0083] From the transfer function S(f) using inverse Fourier
transformation, the impulse response in the time domain can be
calculated at 124. Because of the measuring of a limited band
region, then also present here is the pulse response of the system
to excitation with a band limited impulse, whose form results from
the form of the window function applied for the inverse Fourier
transformation. From the position of the maximum of this delayed
impulse relative to the time axis, the group propagation time
.tau..sub.g within the measured, band limited region can be
ascertained at 125. From this, in simple manner, the propagation
velocity of the signal can be estimated at 126:
c = d .tau. g ##EQU00012##
[0084] In many polar media, dispersion occurs (dependence of the
permittivity and therewith the propagation velocity on the
frequency of the electromagnetic wave). For this reason, the above
estimated, average propagation time in the sense of a group
propagation time is only limitedly suitable for direct determining
of the media properties. In order to enable a precise measuring,
the phase response can be utilized by calculating in the measured
frequency band the phase travel time as a function of frequency at
127:.phi.=arg (S(f))
.tau. p h ( f ) = - d .PHI. ( f ) d f ##EQU00013##
[0085] The ambiguity of the phase response, describable by a whole
number n in .phi..sub.real=.phi..sub.measured+n2
.pi..tau..sub.ph.tau..sub.gr, can be removed by selecting n such
that the deviation between .tau..sub.ph and .tau..sub.gr is
minimum. In this way, now the phase response and, by
c ( f ) = d .tau. p h ( f ) ##EQU00014##
also the exact response of the propagation velocity versus
frequency are determinable at 128. The behavior of the attenuation
d is directly known from the amplitude response of S(f).
[0086] From the now known behaviors of c and .alpha. as expressed
by the following two equations, in 129, these can be directly
converted into the physical variable of the complex valued
permittivity of the medium : *= '+j ''
c = [ .mu. 0 ' 2 [ 1 + ( '' ' ) 2 + 1 ] ] - 1 2 ##EQU00015##
.alpha. = .omega. [ .mu. 0 ' 2 [ 1 + ( '' ' ) 2 - 1 ] ] 1 2
##EQU00015.2##
[0087] where:
[0088] .omega.: angular frequency (.omega.=2.pi.f)
[0089] .mu.: permeability, .mu.=.mu..sub.0.mu..sub.r
[0090] .mu..sub.0: magnetic field constant,
.mu. 0 = 4 .pi. 10 - 7 n a 2 ##EQU00016##
[0091] .mu..sub.r: relative permeability
[0092] .sub.0: electrical field constant,
0 .apprxeq. 8 , 854 10 - 12 As Vm ##EQU00017##
[0093] The values for * and ' determined from the measuring can now
be utilized in equation Eq2, either by using the value at an
earlier defined measuring frequency or by processing the total
measurement data vector in Eq2.
[0094] Based on the above, everything is ready, in order to solve
the system of equations Eq1, Eq2, Eq3 and, thus, to determine the
fractions of the components in the milk, especially the fat
fraction.
[0095] FIG. 4 shows, finally, a measuring arrangement 400 of the
invention for determining the milk fat fraction, especially by
means of the method of the invention. The measuring arrangement 400
includes measuring devices installed in a pipeline 400, namely a
microwave sensor 420, a Coriolis-mass flowmeter 430 for registering
density and mass flow of a medium flowing in the pipeline 410,
especially a Coriolis-mass flowmeter with two bent measuring tubes,
as well as an absolute pressure sensor 440, which has a measured
value output, which is connected to an auxiliary signal input of
the Coriolis mass flowmeter. The measuring arrangement 400
includes, additionally, a computer unit 450, which is connected to
the signal outputs of the microwave sensor 420 and the
Coriolis-mass flowmeter 430. The microwave sensor 420 is adapted,
based on signal travel times, to register permittivity values
and/or absorption of the medium flowing in the pipeline and to
output such to the computer unit 450. The Coriolis-mass flowmeter
430 is adapted to ascertain, besides the mass flow {acute over (m)}
(m-dot), the density, the air fraction a.sub.air and the media
temperature T and to output these to the computer unit 450. The
computer unit 450 is adapted, based on these input variables, to
ascertain the composition of the medium flowing in the pipeline and
to output such under the assumption that the medium is milk.
* * * * *